Constraining Isocurvature Initial Conditions with WMAP 3-year data

TL;DR

The study investigates whether isocurvature initial conditions contribute subdominant or substantial power to cosmological perturbations by analyzing 3-year WMAP CMB data (temperature and polarization) in combination with SDSS and SNLS observations. It employs covariance-based formalisms, including the $\alpha,\beta$ and $z_{ij}$ parameterizations, to model single and multiple isocurvature modes and their correlations, explored with CAMB and Markov Chain Monte Carlo across flat $\Lambda$CDM models. The results show that polarization data tighten single-mode isocurvature constraints, typically limiting $\alpha$ to a few percent and setting lower bounds on the correlated-to-adiabatic ratio $r_{iso}$, while allowing multi-mode scenarios where destructive interference can sustain larger total isocurvature fractions (up to $r_{iso}\approx0.6$ in some cases) absent strong priors. These findings have implications for curvaton and certain double inflation models, and highlight the need for future large-scale polarization and Planck-era data to break degeneracies and more decisively constrain the space of correlated isocurvature initial conditions.

Abstract

We present constraints on the presence of isocurvature modes from the temperature and polarization CMB spectrum data from the WMAP satellite alone, and in combination with other datasets including SDSS galaxy survey and SNLS supernovae. We find that the inclusion of polarization data allows the WMAP data alone, as well as in combination with complementary observations, to place improved limits on the contribution of CDM and neutrino density isocurvature components individually. With general correlations, the upper limits on these sub-dominant isocurvature components are reduced to ~60% of the first year WMAP results, with specific limits depending on the type of fluctuations. If multiple isocurvature components are allowed, however, we find that the data still allow a majority of the initial power to come from isocurvature modes. As well as providing general constraints we also consider their interpretation in light of specific theoretical models like the curvaton and double inflation.

Figures (7)

• Figure 1: 1-dimensional likelihood distributions for CDM (top) and neutrino (bottom) density isocurvature models with perfectly correlated $\beta = 1$, anti-correlated $\beta = -1$ and uncorrelated $\beta =0$ isocurvature perturbations using WMAP only data (black full) and combined with SDSS, SNLS and BBN data (red dashed).
• Figure 2: 68 % and 95 % 2-dimensional constraints on the amplitudes of generally correlated isocurvature modes, for the CI mode (left), the NID mode (center), and the NIV mode (right) for WMAP plus SDSS and SNLS data. The top panels show primordial amplitude contributions in terms of $\alpha,\beta$, using flat priors on ${z_{ij}}$ (line contours) and $\alpha,\beta$ (filled contours). The {$\alpha, 2\beta\sqrt{\alpha(1-\alpha)}$} parameter space is contained within a circle of unit radius shown by the dashed line. The lower panels show the observable CMB power contributions in terms of ${z_{ij}}$.
• Figure 3: The effect of varying the CDM isocurvature spectral index independently for an AD+CI scenario with WMAP plus SDSS and SNLS data: 68 % and 95 % constraints on the AD-CI cross-correlation $\beta$ (left panel), and adiabatic spectral index (right panel). The dotted line in the right panel shows $n_{adi}=n_{iso}$.
• Figure 4: AD+CI: (Top) CMB temperature power spectrum for the best-fit model with correlated AD+CI modes and independent spectral indices (solid) for WMAP plus SDSS and SNLS data. The model has $r_{iso}=3.4\%$, $\alpha=0.49$, $\beta=-0.26$, $n_{adi}=0.97$, $n_{iso}=2.7$, and has $-2\ln {\cal L}$ lower than the best-fit adiabatic model. The contribution of each mode correlation to the total spectrum is shown, including the WMAP data. Bottom: the CMB spectra are compared to the pure adiabatic best-fit model (dashed). Only the $\ell<500$ section of the TE spectrum is shown.
• Figure 5: AD+CI+NID: 2-dimensional constraints show the degeneracy between isocurvature cross-correlation amplitudes $z_{ij}$, and the adiabatic amplitude $z_{AA}$, that allows the destructive interference of isocurvature spectra.